Bulls need a player who is able to create offense for himself, and cares more about scoring (and is good at it) than defending.

Why not put such a troubled, yet talented, player on a strong defensive roster with great leadership? There is zero chance that Beasley can negatively affect the Bulls locker room. It wouldn't be allowed. Absolute worst case scenario is he gets cut/sent to the end of the bench. Best case is he becomes what he was supposed to be -- Poor Man's Melo... say 15-20 ppg on adequate shooting, with little else.